Finiteness in derived categories of local rings

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension, injective dimension, and Gorenstein dimension, are established. It is proved that these specialize to give results concerning modules over complete intersection local rings. A noteworthy feature is the use of techniques based on thick subcategories of derived categories.Comment: 40 pages. Minor revisions. To appear in Commentarii Math. Helvetic

DG algebras with exterior homology

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page

Mass Hierarchy Resolution in Reactor Anti-neutrino Experiments: Parameter Degeneracies and Detector Energy Response

Determination of the neutrino mass hierarchy using a reactor neutrino experiment at $\sim$60 km is analyzed. Such a measurement is challenging due to the finite detector resolution, the absolute energy scale calibration, as well as the degeneracies caused by current experimental uncertainty of $|\Delta m^2_{32}|$. The standard $\chi^2$ method is compared with a proposed Fourier transformation method. In addition, we show that for such a measurement to succeed, one must understand the non-linearity of the detector energy scale at the level of a few tenths of percent.Comment: 7 pages, 6 figures, accepted by PR

Assessment of cockpit interface concepts for data link retrofit

The problem is examined of retrofitting older generation aircraft with data link capability. The approach taken analyzes requirements for the cockpit interface, based on review of prior research and opinions obtained from subject matter experts. With this background, essential functions and constraints for a retrofit installation are defined. After an assessment of the technology available to meet the functions and constraints, candidate design concepts are developed. The most promising design concept is described in detail. Finally, needs for further research and development are identified

Drawing Graphs within Restricted Area

We study the problem of selecting a maximum-weight subgraph of a given graph such that the subgraph can be drawn within a prescribed drawing area subject to given non-uniform vertex sizes. We develop and analyze heuristics both for the general (undirected) case and for the use case of (directed) calculation graphs which are used to analyze the typical mistakes that high school students make when transforming mathematical expressions in the process of calculating, for example, sums of fractions

The application of ultrasonic NDT techniques in tribology

The use of ultrasonic reflection is emerging as a technique for studying tribological contacts. Ultrasonic waves can be transmitted non-destructively through machine components and their behaviour at an interface describes the characteristics of that contact. This paper is a review of the current state of understanding of the mechanisms of ultrasonic reflection at interfaces, and how this has been used to investigate the processes of dry rough surface contact and lubricated contact. The review extends to cover how ultrasound has been used to study the tribological function of certain engineering machine elements

White Paper: Measuring the Neutrino Mass Hierarchy

This white paper is a condensation of a report by a committee appointed jointly by the Nuclear Science and Physics Divisions at Lawrence Berkeley National Laboratory (LBNL). The goal of this study was to identify the most promising technique(s) for resolving the neutrino mass hierarchy. For the most part, we have relied on calculations and simulations presented by the proponents of the various experiments. We have included evaluations of the opportunities and challenges for these experiments based on what is available already in the literature.Comment: White paper prepared for Snowmass-201

Gross-Hopkins duality and the Gorenstein condition

Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this phenomenon in terms of the Gorenstein condition for maps of ring spectra in the sense of [Duality in algebra and topology, Adv. Math. 200 (2006), 357--402. arXiv: math.AT/0510247 ]. We describe a general notion of Brown-Comenetz dualizing module for a map of ring spectra and show that in this context such dualizing modules correspond bijectively to invertible K(n)-local spectra.Comment: 27 pages. Introduction has been revised significantly; minor revisions elsewhere. To appear in the Journal of K-Theor

Comparison of bare root and RPM seedling production technologies : implications for agroforestry

Paper presented at the 12th North American Agroforesty Conference, which was held June 4-9, 2011 in Athens, Georgia.In Ashton, S. F., S.W. Workman, W.G. Hubbard and D.J. Moorhead, eds. Agroforestry: A Profitable Land Use. Proceedings, 12th North American Agroforestry Conference, Athens, GA, June 4-9, 2011.'Root Production Method' (RPM) technology significantly increases the development of root systems in containerized seedlings. As an alternative to bare root seedlings, RPM seedlings have been promoted as a method to increase growth and survivability of hardwood trees. However, few scientific studies have been conducted that would support these claims. Three oak species (Quercus spp.) were the focus of this study. Seed was collected from a single mother tree of black oak (Quercus velutina, Lam.), white oak (Quercus alba Linn.), and swamp white oak (Quercus bicolor Willd.). Half of the seed from each mother tree was used to produce RPM, the other half bare root stock, (i.e. half siblings) which were planted in the fall (RPM) of 1996 or spring (bare root) of 1997 at the Horticulture and Agroforestry Research Center, New Franklin, MO. After 14 years in the field, bare root and RPM trees were harvested for each species and total above ground weight was recorded. Statistical analysis of the data was conducted using least-square means and a method of orthogonal contrasts to determine if significant differences existed between the biomass of bare root and RPM trees. Results showed that the RPM trees had up to twice as much above-ground biomass weight as the bare root trees of the same age. Implications of this study suggest that RPM trees could be used in agroforestry practices as a way of increasing carbon sequestration and biomass production. In addition, the significant increase in growth that was observed should serve to enhance interest in adopting agroforestry practices.Larry D. Godsey (1), John P. Dwyer (2), W. Dusty Walter (1) and Harold 'Gene' Garrett (1) ; 1. University of Missouri Center for Agroforestry, Columbia, MO. 2. Department of Forestry, School of Natural Resources, University of Missouri-Columbia,Columbia, MO.Includes bibliographical references

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione